ZTF Field FlattenerRev 3

P. Jelinsky2012/07/20

Window Thickness

2

• The stress on a window, σ is

• Where ν is the Poisson’s ratio, q is the pressure on the window, d is the window diameter and t is the window thickness

• To first order the allowed stress is independent of the window diameter• Therefore the diameter to thickness ratio must be less than a given value.

• Our mechanical engineer did an analysis and came up with a ratio of 10 (might need to be less at diameter grows)

• The QUEST and PTF camera window has a ratio of 14.4• The window thickness strongly affects the performance of the lens

2

3233

tdq

Assumptions

3

• Distance from flattener to CCD is >= 3mm• Allow distance from corrector to mirror to vary• d/t <= 14.4 (same as QUEST camera)• Flattener is Fused Silica• All spherical surfaces

• Aspheric surfaces did not change performance much• Optimize over 5 wavelengths in the g’, r’ bands as below (allowing a focus change).

• Report results for u’ and i’ band (allowing a focus change)• u’ band seems very narrow (Maybe I read DIQ spreadsheet incorrectly?)

• Optimize over 5 field points, weighted by area

u’ g’ r’ i’Wavelength

(nm)Wavelength

(nm)Wavelength

(nm)Wavelength

(nm)352.0 398.0 593.0 719.5

353.5 432.5 625.5 770.75

355.0 467.0 658.0 822.0

356.5 501.5 690.5 873.25

358.0 536.0 723.0 924.5

Focal Plane Layout

4

• 9 detector focal plane needs a flattener with a radius of 3.8°, a 12 detector focal plane needs a flattener to a radius of 4°, a 16 detector focal plane needs a window to 5°• If field flattener is circular

Layout• No filter added yet

5

Case I Classical Schmidt• About 0.5 arcseconds FWHM for 4 ° radius• About 0.7 arcseconds FWHM for 5 ° radius

— Only changed focus between bands

6

Aver

age

FWHM

arc

seco

nds

0.53

0.8

0.27

0.4

0.67

0.13

Case I Classical Schmidt (cont)

7

# Type Comment ROC=1/c(mm)

Thickness(mm) Glass

SemiDiameter

(mm)Conic=k A2 A4 A6

1STANDARD CORRECTOR 117054.899 11.481LLF6 622.445 0 0 0 02EVENASPH CORRECTOR 64570.285 17.221BK7 623.103 0 0 -5.68497E-12 03EVENASPH CORRECTOR 173900.946 6126.226 624.023 0 0 2.24934E-12 8.01152E-204STANDARD M1 -6123.940 -3000.000MIRROR 901.700 0 0 0 05STANDARD G Focus Infinity -49.411 286.323 0 0 0 06STANDARD R Focus Infinity -49.415 0.000 0 0 0 07STANDARD I Focus Infinity -49.420 0.000 0 0 0 08STANDARD u focus Infinity -49.422 0.000 0 0 0 09STANDARD FILM -3067.135 0.000 268.016 0 0 0 0

88

66

44

2222

2

)1(11rArArArA

rck

crz

Case II Curved FP with lens (D/t = 14.4)• About 1.3 arcseconds FWHM for 4 ° radius• About 1.5 arcseconds FWHM for 5 ° radius

— Only changed focus between bands

8

Aver

age

FWHM

arc

seco

nds

1.0

1.7

0.3

0.7

1.3

Case II Curved FP with lens (D/t = 14.4) (cont)

9

# Type Comment ROC=1/c(mm)

Thickness(mm) Glass

SemiDiameter

(mm)Conic=k A2 A4 A6

1STANDARD CORRECTOR 117054.899 11.481LLF6 622.445 0 0 0 02EVENASPH CORRECTOR 64570.285 17.221BK7 623.091 0 0 -5.68497E-12 03EVENASPH CORRECTOR 173900.946 6048.159 623.999 0 0 2.24934E-12 8.01152E-204STANDARD M1 -6123.940 -2950.000MIRROR 901.700 0 0 0 05STANDARD G Focus Infinity -70.535 0.000 0 0 0 06STANDARD R Rocus Infinity -70.462 0.000 0 0 0 07STANDARD I Focus Infinity -70.438 0.000 0 0 0 08STANDARD U Focus Infinity -70.644 301.098 0 0 0 09STANDARD Flattener -1332.883 -37.755SILICA 271.804 0 0 0 0

10STANDARD 30094.311 -3.000 269.516 0 0 0 011STANDARD FILM -13654.499 0.000 266.662 0 0 0 0

88

66

44

2222

2

)1(11rArArArA

rck

crz

Case IIa Curved FP with lens (D/t = 25)• About 0.9 arcseconds FWHM for 4 ° radius• About 1.2 arcseconds FWHM for 5 ° radius

— Only changed focus between bands

10

Aver

age

FWHM

arc

seco

nds

0.8

1.3

0.3

0.5

1.1

Case IIa Curved FP with lens (D/t = 25) (cont)

11

# Type Comment ROC=1/c(mm)

Thickness(mm) Glass

SemiDiameter

(mm)Conic=k A2 A4 A6

1STANDARD CORRECTOR 117054.899 11.481LLF6 622.445 0 0 0 02EVENASPH CORRECTOR 64570.285 17.221BK7 623.103 0 0 -5.68497E-12 03EVENASPH CORRECTOR 173900.946 6092.760 624.023 0 0 2.24934E-12 8.01152E-204STANDARD M1 -6123.940 -2950.000MIRROR 901.700 0 0 0 05STANDARD G Focus Infinity -81.635 301.211 0 0 0 06STANDARD R Rocus Infinity -81.593 0.000 0 0 0 07STANDARD I Focus Infinity -81.581 0.000 0 0 0 08STANDARD U Focus Infinity -81.703 0.000 0 0 0 09STANDARD -1838.511 -21.670SILICA 270.870 0 0 0 0

10STANDARD -10712.343 -3.000 269.623 0 0 0 011STANDARD FILM -5534.668 0.000 267.408 0 0 0 0

88

66

44

2222

2

)1(11rArArArA

rck

crz

Case III Flat FP single lens (D/T = 14.4)• About 1.3 arcsecond FWHM for 4° radius • About 1.8 arcsecond for 5 ° radius

— Only focus changed between bands

12

Aver

age

FWHM

arc

seco

nds

1

2

Case III Flat FP single lens (D/T = 14.4) (cont)

13

# Type Comment ROC=1/c(mm)

Thickness(mm) Glass

SemiDiameter

(mm)Conic=k A2 A4 A6

1STANDARD CORRECTOR 117054.899 11.481LLF6 622.445 0 0 0 02EVENASPH CORRECTOR 64570.285 17.221BK7 623.091 0 0 -5.68497E-12 03EVENASPH CORRECTOR 173900.946 6026.254 623.999 0 0 2.24934E-12 8.01152E-204STANDARD M1 -6123.940 -3000.000MIRROR 901.700 0 0 0 05STANDARD G band focus Infinity -17.198 0.000 0 0 0 06STANDARD R band Focus Infinity -17.130 0.000 0 0 0 07STANDARD I band focus Infinity -17.106 0.000 0 0 0 08STANDARD u band focus Infinity -17.303 286.231 0 0 0 09STANDARD 0 -1114.481 -42.523SILICA 271.182 0 0 0 0

10STANDARD 0 9059.173 -3.000 269.772 0 0 0 011STANDARD FILM Infinity 0.000 266.590 0 0 0 0

88

66

44

2222

2

)1(11rArArArA

rck

crz

Case IV split flat FP (D/T = 14.4)• About 1.2 arcsecond FWHM for 4° radius • About 1.8 arcsecond for 5 ° radius

— Only focus changed between bands

14

Aver

age

FWHM

arc

seco

nds

1

2

Case IV split flat FP (D/T = 14.4) (cont)

15

# Type Comment ROC=1/c(mm)

Thickness(mm) Glass

SemiDiameter

(mm)Conic=k A2 A4 A6

1STANDARD CORRECTOR 117054.899 11.481LLF6 622.445 0 0 0 02EVENASPH CORRECTOR 64570.285 17.221BK7 623.091 0 0 -5.68497E-12 03EVENASPH CORRECTOR 173900.946 6026.255 623.999 0 0 2.24934E-12 0.000004STANDARD M1 -6123.940 -3000.000MIRROR 901.700 0 0 0 05STANDARD G band focus Infinity -17.198 0.000 0 0 0 06STANDARD R band Focus Infinity -17.130 0.000 0 0 0 07STANDARD I band focus Infinity -17.106 0.000 0 0 0 08STANDARD u band focus Infinity -17.303 286.231 0 0 0 09STANDARD 0 -1114.474 -42.523SILICA 271.182 0 0 0 0

10STANDARD 0 9059.535 -3.000 269.772 0 0 0 011STANDARD FILM Infinity 0.000 266.590 0 0 0 0

0 0 0Infinity 0.000 0.000 0 0 0 0

88

66

44

2222

2

)1(11rArArArA

rck

crz

Case V 4 segment (16 CCD) FP (D/T = 14.4)

• Each quadrant is flat but tilted— Forms the peak of a 4 sided pyramid

• Each Quadrant has a vacuum field flattener in front

• 16 total detectors

16

Case V (cont)

17

R Band Imaging over ¼ of field

Band FWHMg’ 21.4 µm (1.43”)

r’ 19.2 µm (1.28”)

i’ 17.6 µm (1.17”)

u’ 17.5 µm (1.17”)

Case V (cont)

18

# Type Comment ROC=1/c(mm)

Thickness(mm) Glass

SemiDiameter

(mm)Conic=k A2 A4 A6 A8

1STANDARD CORRECTOR 117054.899 11.481LLF6 622.454 0 0 0 0 02EVENASPH CORRECTOR 64570.285 17.221BK7 623.143 0 0 -5.68497E-12 0 03EVENASPH CORRECTOR 173900.946 6103.022 624.109 0 0 2.24934E-12 8.01152E-20 04STANDARD M1 -6123.940 -3000.000MIRROR 901.700 0 0 0 0 05STANDARD G band focus Infinity -36.762 0.000 0 0 0 0 06STANDARD R band Focus Infinity -36.712 0.000 0 0 0 0 07STANDARD I band focus Infinity -36.697 0.000 0 0 0 0 08STANDARD u band focus Infinity -36.841 303.990 0 0 0 0 0

DX DY θx θy9COORDBRK 0.000 0.000 0 105.66 105.44 -1.96 1.96

10STANDARD FLATTENER -1043.178 -19.394SILICA 139.620 0 0 0 0 011STANDARD 16214.427 -3.000 139.620 0 0 0 0 012STANDARD FILM Infinity 0.000 136.459 0 0 0 0 0

88

66

44

2222

2

)1(11rArArArA

rck

crz

Summary• The 4 segment focal plane performs as well as a curved focal plane with a vacuum lens

19

Aver

age

FWHM

arc

seco

nds

0.33

1.33

0.67

1.00

1.67